How do you denote the dihedral group of order n?

This is not a question of “vim or emacs” or “tabs or spaces” sort, but still there are two notations in use. Some sources use D_n to denote a dihedral group of order n, and some others – a dihedral group of order 2n. Both notations are also reflected in mathematical software.

For example, in GAP DihedralGroup(n) returns a group of order n:

and in SageMath – a group of order 2n:

Let us look at other systems: (more…)